JEE Questions for Maths Sequences And Series Quiz 15

0%
A.P
0%
G.P
0%
H.P
0%
None of these

0%
In H.P
0%
In G.P
0%
In A.P
0%
None of these

If a,b,c are in H.P., then for all n ϵ N the true statement is

0%
an + cn < 2bn
0%
an + cn > 2bn
0%
an + cn = 2bn
0%
None of these

If the product of three terms of G.P. if 512. If 8 added to first and 6 added to second term, so that number may be in A.P., then the numbers are

0%
2,4,8
0%
4,8,16
0%
3,6,12
0%
None of these

Let a be a positive number such that the arithmetic mean of a and 2 exceeds their geometric mean be 1.Then, the value of a is

0%
3
0%
5
0%
9
0%
8
0%
10

0%
A.P
0%
G.P
0%
H.P
0%
None of these

Three non-zero real numbers form A.P. and the squares of these numbers taken in the same order form a G.P. Then the number of all possible common ratios of the G.P. is

0%
1
0%
2
0%
3
0%
None of these

0%
0%
A
0%
2A
0%
None of these

0%
A.P
0%
G.P
0%
H.P
0%
None of these

0%
A.P
0%
G.P
0%
H.P
0%
None of these

The sum of three decreasing numbers in A.P. is 27. If –1, – 1, 3 are added to them respectively, the resulting series is in G.P. The numbers are

0%
5,9,13
0%
15,9,3
0%
13,9,5
0%
17,9,1

0%
0%
2)
0%
(and (both are true
0%
None of the above

0%
1
0%
0
0%
2
0%
3

0%
A.P
0%
G.P
0%
H.P
0%
None of these

If a,b,c are in A.P., then 2^{ax + 1} , 2^{bx + 1}, 2^{cx + 1} , x ≠ 0 are in

0%
A.P
0%
G.P only when x > 0
0%
G.P if x < 0
0%
G.P for all x ≠ 0

0%
0%
2)
0%
0%
None of the above

If a, b, c are in A.P and a², b², c² are in H.P., then

0%
a ≠ b ≠ c
0%
2)
0%
a, b, c are in G.P
0%

If a₁ a₂ ...... a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + ....... + a_{n - 1} + 2a_n is

0%
n(2c)1/n
0%
(n + 1)c1/n
0%
2nc1/n
0%
(n + 1)(2c)1/n

If arithmetic mean of two positive numbers is A, their geometric mean is G and harmonic mean is H, then H is equal to

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

If the first, second and last terms of an arithmetic series are a,b and c respectively then the number of terms is

0%
0%
2)
0%
0%

0%
1056
0%
1088
0%
1120
0%
1332
0%
Both (and (4)

0%
0%
2)
0%
0%

If the p^th ,q^th and r^th term of an arithmetic sequence are a,b and c respectively, then the value of [a (q – r) + b(r – p) + c(p – q)] =

0%
1
0%
–1
0%
0
0%
1/2

If a_m denotes the m^th term of an A.P then a_m

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
1
0%
0

If 1, log₉ (3^{1– x} + 2), log₃(4.3^x –are in A.P then x equals

0%
log3 4
0%
1 – log3 4
0%
1 – log4 3
0%
log4 3

If a,b,c,d,e are in A.P. then the value of a + b + 4c – 4d + e in terms of a, if possible is

0%
4a
0%
2a
0%
3
0%
None of these

Four numbers are in arithmetic progression. The sum of first and last term is 8 and the product of both middle terms is 15. The least number of the series is

0%
4
0%
3
0%
2
0%
1

The interior angles of a polygon are in A.P. If the smallest angle be 120^o and the common difference be 5°, then the number of sides of the polygon

0%
8
0%
10
0%
9
0%
6

The sum of first n natural number is

0%
n(n – 1)
0%
2)
0%
n(n + 1)
0%

If n be odd or even, then sum of n terms of the series 1 – 2 + 3 – 4 + 5 – 6 + ...... will be

0%
0%
2)
0%
0%
0%
Both (and (3)

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent month his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

0%
18 months
0%
19 months
0%
20 months
0%
21 months

The ratio of sum of m and n terms of an A.P. is m² : n², then the ratio of m^th and n^th term will be

0%
0%
2)
0%
0%

If S_n denotes the sum of n terms of an arithmetic progression, then the value of (S_2n – S_n) is equal to

0%
2Sn
0%
S3n
0%
0%

0%
x = 3
0%
x = 4√3
0%
x = 9
0%
x = √3

If S_k denotes the sum of first k terms of an arithmetic progression whose first term and common difference are a and b respectively, then S_kn/S_n be independent of n if